Arithmetic mean by _________ is the sum of all observations in a series divided by the total number of observations.

assumed mean method

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direct method

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step deviation method

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none of the above

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Solution

The correct option is B direct method
The direct method of finding the arithmetic mean involves finding the ratio of the sum of total observations to the number of observations.

A worked example:
Find the arithmetic mean of numbers: 5, 9, 8, 3, 7

$¯ X = \frac{5 + 9 + 8 + 3 + 7}{5}$
$¯ X = \frac{32}{5}$
$¯ X = 6.4$

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State with reason whether the following statements are True or False:

(i) Sum of square of the deviations of items from their arithmetic mean is the maximum.

(ii) Standard Deviation is based on all values.

(iii) For a given set of observations, standard deviation is always more than mean deviation from mean.

Consider a grouped data distribution for which the mean is found by assumed mean method.

P = sum of the products of ‘d’ and frequency for each class interval

Here $d_{i} = x_{i} - A$

Q = total number of observations

A = assumed mean

M = mean of given grouped data distribution

Which of the following statements is true?

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